Indiana University - Purdue University Fort Wayne
Opus: Research & Creativity at IPFW
Manufacturing and Construction Engineering Department of Manufacturing and Construction
Technology Faculty Publications Engineering Technology
8-2016
Applied Strength of Materials for Engineering
Technology
Barry Dupen
Indiana University - Purdue University Fort Wayne,
Follow this and additional works at: http://opus.ipfw.edu/mcetid_facpubs
Part of the Applied Mechanics Commons
This edition has been superseded.
Opus Citation
Barry Dupen (2016). Applied Strength of Materials for Engineering Technology. 10 ed. Purdue University.
http://opus.ipfw.edu/mcetid_facpubs/48
This Book is brought to you for free and open access by the Department of Manufacturing and Construction Engineering Technology at Opus:
Research & Creativity at IPFW. It has been accepted for inclusion in Manufacturing and Construction Engineering Technology Faculty Publications by
an authorized administrator of Opus: Research & Creativity at IPFW. For more information, please contact .
,Applied Strength of Materials for
Engineering Technology
Barry Dupen
Associate Professor, Mechanical Engineering Technology, Indiana University – Purdue University Fort Wayne
v.10 Revised August 2016. This work is licensed under Creative Commons Attribution-ShareAlike 4.0
International (CC BY-SA 4.0) See creativecommons.org for license details.
1
,Table of Contents
Preface...............................................................................................3 Shear Stress in Beams...............................................................87
Purpose of the Book....................................................................3 Allowable Load.........................................................................92
Editors.........................................................................................4 Chapter 10: Beam Deflection.........................................................94
Cover Photos...............................................................................5 Radius of Curvature..................................................................94
Terminology......................................................................................6 The Formula Method for Simple Cases...................................95
Definitions.........................................................................................9 Formula Method Hints..............................................................98
Chapter 1: Introduction to Strength of Materials...........................11 The Formula Method for Complex Cases: Superposition.......98
What is Strength of Materials?.................................................11 Visualizing the Deflection Curve...........................................100
The Factor-Label Method of Unit Conversion........................12 Chapter 11: Beam Design.............................................................102
Chapter 2: Stress and Strain............................................................17 Wide-Flange Steel Beam Design in Six Easy Steps..............102
Normal Stress and Strain..........................................................17 Timber Beam Design in Six Easy Steps................................108
Sign Convention.......................................................................19 All Other Beams.....................................................................110
Shear Stress and Strain.............................................................20 Chapter 12: Combined Stresses....................................................112
Chapter 3: Poisson's Ratio and Thermal Expansion......................23 Tension + Bending..................................................................112
Poisson's Ratio..........................................................................23 Bending in Two Directions....................................................112
Thermal Expansion and Thermal Stress..................................25 Eccentric Loading...................................................................114
Chapter 4: Pressure Vessels and Stress Concentrations................28 Chapter 13: Statically Indeterminate Beams................................118
Thin-Walled Pressure Vessels..................................................28 Defining Determinate and Indeterminate Beams..................118
Stress Concentration in Tension...............................................30 Method of Superposition........................................................118
Chapter 5: Bolted and Welded Joints.............................................33 Chapter 14: Buckling of Columns................................................124
Bolted Lap Joints Loaded in Tension......................................33 Types of Columns...................................................................124
Welded Lap Joints....................................................................38 Ideal Slender Columns...........................................................124
Chapter 6: Properties of Areas........................................................41 Structural Steel Columns........................................................126
Dimensions and Area................................................................41 Steel Machine Parts................................................................127
Centroid and Centroidal Axes..................................................41 Chapter 15: Visualizing Stress and Strain....................................130
Moment of Inertia of a Rectangle............................................41 Measuring Stress.....................................................................130
Compound Beams Sharing a Centroidal Axis.........................42 Stress at the Base of a Short Block........................................130
Hollow Beams Sharing a Centroidal Axis...............................43 Mohr's Circle...........................................................................131
The Transfer Formula...............................................................44 Bibliography..................................................................................148
Compound Beams With Different Neutral Axes.....................45 Textbooks................................................................................148
Hollow Beams With Different Neutral Axes...........................48 Other Reading Material..........................................................148
Moment of Inertia about the y-y Neutral Axis........................51 Appendix A: Units........................................................................149
Shortcuts....................................................................................54 SI System of Units..................................................................149
Radius of Gyration....................................................................54 US Customary System of Units.............................................149
Polar Moment of Inertia...........................................................54 Appendix B: Materials Properties................................................150
Chapter 7: Torsion in Round Shafts...............................................55 Metals, Concrete, & Stone.....................................................150
Shear Stress in a Round Shaft..................................................55 Appendix C: Properties of Areas..................................................154
Angle of Twist in a Round Shaft..............................................57 Center of Gravity, Area, Moment of Inertia, and Radius of
Stress Concentration in Torsion...............................................58 Gyration..................................................................................154
Chapter 8: Beam Reactions, Shear Diagrams, and Moment Appendix D: Properties of Steel Beams and Pipes......................157
Diagrams..........................................................................................60 W-beams.................................................................................157
Loads on Beams........................................................................60 Steel Pipes...............................................................................161
Reactions for Simply-Supported Simple Beams.....................61 Copper Tubing........................................................................162
Reactions for Overhanging and Cantilever Beams..................64 Appendix E: Mechanical and Dimensional Properties of Wood.163
Shear Diagrams.........................................................................66 Mechanical Properties of Air-Dried Boards and Timber......163
Moment Diagrams....................................................................72 Softwood Lumber and Timber Sizes.....................................164
Chapter 9: Stresses in Beams..........................................................82 Appendix F: Beam Equations.......................................................166
Bending Stress in Beams..........................................................82 Index..............................................................................................171
Bending Stress in Wide-Flange Steel Beams..........................84 Index..............................................................................................171
2
, Preface
Preface
Purpose of the Book
1.9 million bachelors degrees are awarded annually in the US.1 About 92 thousand are Engineering degrees, and about 17
thousand are Engineering Technology degrees and Technician degrees. The number of Mechanical, Civil, and Construction
Engineering Technology graduates is only about 2 thousand per year, so the market for algebra-based Strength of Materials
textbooks for Engineering Technology is a small fraction of the market for calculus-based Engineering textbooks.
Since I attended college in the 1980s, textbook prices have risen about twice as fast as inflation. The internet did not exist
back then, so all textbooks were printed. Now we have another option: low-cost or free online e-books which are revised
more frequently than printed books. While traditional textbooks are revised every 4 to 10 years based on input from experts
in the topic, this e-book is revised every semester based on input from experts in learning: the students.
Students complain that the explanations in many Engineering Technology textbooks are too theoretical, too wordy, and too
difficult to understand. They also complain about the lack of complete unit conversions in example problems, and
inconsistent use of symbols between related courses. For example, some authors use sn, ss, and e for normal stress, shear
stress, and strain, instead of the standard Greek symbols σ, τ, and ε. This use of Latin characters with multiple subscripts
confuses students because the Greek symbols are used in other textbooks, and because capital S is used for section modulus
later in the course. Students have trouble distinguishing between s and S on the chalkboard and in their notes.
Professors complain that too many students copy answers from online solution manuals or fraternity homework files instead
of learning to solve problems from scratch, then these students fail exams. Probably 10% of the learning in Strength of
Materials occurs in class, and 90% occurs as students solve problems. Deliberately, the problem set for this book is not
available online, and is changed every semester.
I teach Strength of Materials to Mechanical and Construction Engineering Technology students. These students tell me they
want help with algebra skills, unit conversions, and problem-solving approaches. The problem set that accompanies this
book contains problems requiring an algebraic answer as well as traditional problems requiring a numerical answer. The
Factor-Label Method of Unit Conversion is emphasized from the first chapter, and is used in all example problems.
Summarizing, the goals of this book are:
• Free distribution over the internet
• Frequent revisions based on student input
• Concise explanations
• Examples with complete unit conversions
• Standard Greek symbols for stress and strain
• Problems requiring algebraic answers as well as problems requiring numerical answers
• Problems requiring answers in sentences to show reasoning and understanding of the topics
This e-book is revised on an ongoing basis. Please send suggestions for improvement to me at .
Barry Dupen
Indiana University – Purdue University Fort Wayne
Fort Wayne, Indiana
August, 2016
1 Data from 2013-2014. Current numbers are in the Digest of Educational Statistics, published by the National Center for Educational
Statistics, U.S. Department of Education, at nces.ed.gov.
3
Opus: Research & Creativity at IPFW
Manufacturing and Construction Engineering Department of Manufacturing and Construction
Technology Faculty Publications Engineering Technology
8-2016
Applied Strength of Materials for Engineering
Technology
Barry Dupen
Indiana University - Purdue University Fort Wayne,
Follow this and additional works at: http://opus.ipfw.edu/mcetid_facpubs
Part of the Applied Mechanics Commons
This edition has been superseded.
Opus Citation
Barry Dupen (2016). Applied Strength of Materials for Engineering Technology. 10 ed. Purdue University.
http://opus.ipfw.edu/mcetid_facpubs/48
This Book is brought to you for free and open access by the Department of Manufacturing and Construction Engineering Technology at Opus:
Research & Creativity at IPFW. It has been accepted for inclusion in Manufacturing and Construction Engineering Technology Faculty Publications by
an authorized administrator of Opus: Research & Creativity at IPFW. For more information, please contact .
,Applied Strength of Materials for
Engineering Technology
Barry Dupen
Associate Professor, Mechanical Engineering Technology, Indiana University – Purdue University Fort Wayne
v.10 Revised August 2016. This work is licensed under Creative Commons Attribution-ShareAlike 4.0
International (CC BY-SA 4.0) See creativecommons.org for license details.
1
,Table of Contents
Preface...............................................................................................3 Shear Stress in Beams...............................................................87
Purpose of the Book....................................................................3 Allowable Load.........................................................................92
Editors.........................................................................................4 Chapter 10: Beam Deflection.........................................................94
Cover Photos...............................................................................5 Radius of Curvature..................................................................94
Terminology......................................................................................6 The Formula Method for Simple Cases...................................95
Definitions.........................................................................................9 Formula Method Hints..............................................................98
Chapter 1: Introduction to Strength of Materials...........................11 The Formula Method for Complex Cases: Superposition.......98
What is Strength of Materials?.................................................11 Visualizing the Deflection Curve...........................................100
The Factor-Label Method of Unit Conversion........................12 Chapter 11: Beam Design.............................................................102
Chapter 2: Stress and Strain............................................................17 Wide-Flange Steel Beam Design in Six Easy Steps..............102
Normal Stress and Strain..........................................................17 Timber Beam Design in Six Easy Steps................................108
Sign Convention.......................................................................19 All Other Beams.....................................................................110
Shear Stress and Strain.............................................................20 Chapter 12: Combined Stresses....................................................112
Chapter 3: Poisson's Ratio and Thermal Expansion......................23 Tension + Bending..................................................................112
Poisson's Ratio..........................................................................23 Bending in Two Directions....................................................112
Thermal Expansion and Thermal Stress..................................25 Eccentric Loading...................................................................114
Chapter 4: Pressure Vessels and Stress Concentrations................28 Chapter 13: Statically Indeterminate Beams................................118
Thin-Walled Pressure Vessels..................................................28 Defining Determinate and Indeterminate Beams..................118
Stress Concentration in Tension...............................................30 Method of Superposition........................................................118
Chapter 5: Bolted and Welded Joints.............................................33 Chapter 14: Buckling of Columns................................................124
Bolted Lap Joints Loaded in Tension......................................33 Types of Columns...................................................................124
Welded Lap Joints....................................................................38 Ideal Slender Columns...........................................................124
Chapter 6: Properties of Areas........................................................41 Structural Steel Columns........................................................126
Dimensions and Area................................................................41 Steel Machine Parts................................................................127
Centroid and Centroidal Axes..................................................41 Chapter 15: Visualizing Stress and Strain....................................130
Moment of Inertia of a Rectangle............................................41 Measuring Stress.....................................................................130
Compound Beams Sharing a Centroidal Axis.........................42 Stress at the Base of a Short Block........................................130
Hollow Beams Sharing a Centroidal Axis...............................43 Mohr's Circle...........................................................................131
The Transfer Formula...............................................................44 Bibliography..................................................................................148
Compound Beams With Different Neutral Axes.....................45 Textbooks................................................................................148
Hollow Beams With Different Neutral Axes...........................48 Other Reading Material..........................................................148
Moment of Inertia about the y-y Neutral Axis........................51 Appendix A: Units........................................................................149
Shortcuts....................................................................................54 SI System of Units..................................................................149
Radius of Gyration....................................................................54 US Customary System of Units.............................................149
Polar Moment of Inertia...........................................................54 Appendix B: Materials Properties................................................150
Chapter 7: Torsion in Round Shafts...............................................55 Metals, Concrete, & Stone.....................................................150
Shear Stress in a Round Shaft..................................................55 Appendix C: Properties of Areas..................................................154
Angle of Twist in a Round Shaft..............................................57 Center of Gravity, Area, Moment of Inertia, and Radius of
Stress Concentration in Torsion...............................................58 Gyration..................................................................................154
Chapter 8: Beam Reactions, Shear Diagrams, and Moment Appendix D: Properties of Steel Beams and Pipes......................157
Diagrams..........................................................................................60 W-beams.................................................................................157
Loads on Beams........................................................................60 Steel Pipes...............................................................................161
Reactions for Simply-Supported Simple Beams.....................61 Copper Tubing........................................................................162
Reactions for Overhanging and Cantilever Beams..................64 Appendix E: Mechanical and Dimensional Properties of Wood.163
Shear Diagrams.........................................................................66 Mechanical Properties of Air-Dried Boards and Timber......163
Moment Diagrams....................................................................72 Softwood Lumber and Timber Sizes.....................................164
Chapter 9: Stresses in Beams..........................................................82 Appendix F: Beam Equations.......................................................166
Bending Stress in Beams..........................................................82 Index..............................................................................................171
Bending Stress in Wide-Flange Steel Beams..........................84 Index..............................................................................................171
2
, Preface
Preface
Purpose of the Book
1.9 million bachelors degrees are awarded annually in the US.1 About 92 thousand are Engineering degrees, and about 17
thousand are Engineering Technology degrees and Technician degrees. The number of Mechanical, Civil, and Construction
Engineering Technology graduates is only about 2 thousand per year, so the market for algebra-based Strength of Materials
textbooks for Engineering Technology is a small fraction of the market for calculus-based Engineering textbooks.
Since I attended college in the 1980s, textbook prices have risen about twice as fast as inflation. The internet did not exist
back then, so all textbooks were printed. Now we have another option: low-cost or free online e-books which are revised
more frequently than printed books. While traditional textbooks are revised every 4 to 10 years based on input from experts
in the topic, this e-book is revised every semester based on input from experts in learning: the students.
Students complain that the explanations in many Engineering Technology textbooks are too theoretical, too wordy, and too
difficult to understand. They also complain about the lack of complete unit conversions in example problems, and
inconsistent use of symbols between related courses. For example, some authors use sn, ss, and e for normal stress, shear
stress, and strain, instead of the standard Greek symbols σ, τ, and ε. This use of Latin characters with multiple subscripts
confuses students because the Greek symbols are used in other textbooks, and because capital S is used for section modulus
later in the course. Students have trouble distinguishing between s and S on the chalkboard and in their notes.
Professors complain that too many students copy answers from online solution manuals or fraternity homework files instead
of learning to solve problems from scratch, then these students fail exams. Probably 10% of the learning in Strength of
Materials occurs in class, and 90% occurs as students solve problems. Deliberately, the problem set for this book is not
available online, and is changed every semester.
I teach Strength of Materials to Mechanical and Construction Engineering Technology students. These students tell me they
want help with algebra skills, unit conversions, and problem-solving approaches. The problem set that accompanies this
book contains problems requiring an algebraic answer as well as traditional problems requiring a numerical answer. The
Factor-Label Method of Unit Conversion is emphasized from the first chapter, and is used in all example problems.
Summarizing, the goals of this book are:
• Free distribution over the internet
• Frequent revisions based on student input
• Concise explanations
• Examples with complete unit conversions
• Standard Greek symbols for stress and strain
• Problems requiring algebraic answers as well as problems requiring numerical answers
• Problems requiring answers in sentences to show reasoning and understanding of the topics
This e-book is revised on an ongoing basis. Please send suggestions for improvement to me at .
Barry Dupen
Indiana University – Purdue University Fort Wayne
Fort Wayne, Indiana
August, 2016
1 Data from 2013-2014. Current numbers are in the Digest of Educational Statistics, published by the National Center for Educational
Statistics, U.S. Department of Education, at nces.ed.gov.
3
